How To Add Complex Numbers

How do you add Complex Numbers


Video Tutorial on Adding Complex Numbers

Let's add the following 2 complex numbers (5 + 2i ) + (7 + 12i) Step 1

Group the real part of the complex number and the imaginary part of the complex number.

(5 + 7) + (2i + 12i)

Step 2

Combine the like terms and simplify

12 + 14i

Practice Problems

Problem 1

Add the following complex numbers: (5 + 3i) + ( 2 + 7i)

Step 1

This problem is very similar to example 1


Group the real part of the complex number and the imaginary part of the complex number.

(5 + 2) + (3i + 7i)

Step 2

Combine the like terms and simplify

7 + 10i

Problem 2

Add the following 2 complex numbers (9 + 11i) + (3 + 5i)

Step 1

This problem is very similar to example 1


Group the real part of the complex number and the imaginary part of the complex number.

(9 + 3) + (11i + 5i)

Step 2

Combine the like terms and simplify

12 + 16i

Problem 3

Add the complex numbers below (12 + 14i) + (3 -2i)

Step 1

This problem is very similar to example 1 with the added twist that we have a negative number in there (-2i).


Group the real part of the complex number and the imaginary part of the complex number.

(12 + 3) + (14i + -2i)

Step 2

Combine the like terms and simplify

15 + 12i

Problem 4

Add the following 2 complex numbers (6 - 13i) + (12 + 8i)

Step 1

This problem is very similar to example 1with the added twist that we have a negative number in there (-13i).


Group the real part of the complex number and the imaginary part of the complex number.

(6 + 12) + (-13i + 8i)

Step 2

Combine the like terms and simplify

18 - 5i

Problem 5

Add the following complex numbers: (-2 - 15i) + (-12 + 13i)

Step 1

Group the real part of the complex number and the imaginary part of the complex number.

(-2 + -12) + (-15i + 13i)

Step 2

Combine the like terms and simplify

-14 + 2i


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